My understanding is AD's treat primarily the depressive episodes with BP, and mood stabilizers are used to keep mania, the highs, in check.
That's my understanding, and that's how it worked out for me.
I took remeron(an AD) and lithium (an MS) for a while and was still beyond struggling.
Started wellbutrin a little while back and i can honestly say now i'm not sure i'd be alive without it, it took me out the lowest of lows